Maximum performance take-off director



Aug 17, 1965 c. A. NEUENDORF ETAL 3,200,542

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MAXIMUM PERFORMANCE TAKE-OFF DIRECTOR Filed June 25, 1962 16 Sheets-Sheet 13 Aug. 17, 1965 c. A. NEUENDORF ETAL 3 0,

MAXIMUM PERFORMANCE TAKE-OFF DIRECTOR I6 Sheets-Sheet 15 Filed June 25, 1962 &

Aug. 17, 1965 c. A. NEUENDORF ETAL 3,200,642

MAXIMUM PERFORMANCE TAKE-OFF DIRECTOR 1e Sheets-Sheet 16 Filed June 25, 1962 Quh \SwM United States Patent 3,200,642 MAXIMUM PERFGRMANCE TAKE-SPF DIRECTOR Charles A. Neuendorf, Toledo, Ohio (Box 9273, Wright- Patterson AFB, ()hio), and William G. Moretti, .hz, 17 Princeton Road, Burlington, Mass.

Filed June 25, 1962, Ser. No. 205,135 4 Claims. (Cl. 73-178) (Granted under Title 35, US. Code (1952), sec. 266) The invention described herein may be manufactured and used by or for the United States Government for governmental purposes without payment to us of any royalty thereon.

The purpose of this invention is to provide a director which will enable a pilot to obtain maximum take-off performance without visual reference to the ground.

Investigations leading to the design of the director established that maximum performance results when the takeoff is accomplished in two phases, in the first of which a constant angle of attack is maintained and in the second of which a constant velocity is maintained, and in which the transition from the first phase to the second phase occurs when the acceleration of the aircraft has fallen to zero. Briefly, the director described herein is a device to enable the pilot to control the aircraft in such manner as to take off in accordance with the above-stated program.

Accurate take-off instrumentation is especially important in the case of large heavily-loaded aircraft. In such aircraft, establishing the correct attitude for lift-off is of primary concern. For example, in the KC-135, a lift off attitude error of only two degrees can either extend the ground roll by 3200 feet or result in take-off flight perilously close to stall conditions, depending upon the direction of the error. This situation makes the use of an attitude gyro, the instrument usually employed to supply pitch information during take-off, undesirable since the indication of this instrument is affected by the acceleration of the aircraft during ground roll, with the result that an erroneous indication of the lift-off attitude may be given. In order to avoid this source of error, the director described herein obtains pitch information from an angle-of-attack sensor which is unaffected by acceleration, the pitch angle and the angle of attack being equal during ground-roll.

The invention will be described in more detail with reference to the accompanying drawings in which:

FIG. 1 illustrates the flight path angles of an aicraft,

FIG. 2 shows the forces and moments acting on an aircraft, 7

FIG. 3 shows the excess thrust available at various airspeeds for a typical cargo aircraft,

FIG. 4 shows time plots of V, V, a and 'y for a constant pitch angle take-off,

FIG. 5 shows altitude vs. distance at reduced thrust for a constant pitch angle take-off,

FIG. 6 shows altitude vs. distance for take-offs at constant pitch angles of various values,

FIG. 7 shows the effects of various lift-off speeds in constant angle take-offs,

FIG. 8 shows time plots of V, V, 7i and 'y for a typical take-off with constant angle of attack,

FIG. 9 gives plots of altitude vs. distance for take-offs at various constant angles of attack,

FIG. 10 shows the effects of various lift-off speeds using a constant angle of attack,

FIGS. 11a and 11b show take-off flight paths for various variables in a typical aircrafts equations of motion,

FIG. 12 shows altitude vs. distance for constant velocity take-offs under various thrust conditions,

FIG. 13 shows time plots of V, V, 'y and a for a takeoff at constant velocity,

FIGS. 14 and f5 shows the take-off performance of a typical aircraft controlled by a flight director in accordance with the invention,

FIG. 16 is a logical diagram of a flight director in accordance with the invention,

FIG. 17 shows a practical embodiment of the system shown in FIG. 16, and

FIG. 18 shows a suitable rectifier for use in FIG. 17.

The following symbols are used in the specification:

0 pitch angle 7 flight path angle 7 rate of change of flight path on angle of attack V velocity V acceleration D drag L lift W weight T thrust in mass M moment I moment of inertia V lift-off velocity V stall velocity KTS knots 11 height h) rate of climb FLIGHT MECHANICS To better follow the various stages leading to the development of the take-off indicator described herein, a review of flight mechanics and the take-off problem is desirable, together with an analysis of the vertical gyro and the angle-of-attack indicator presently used as pitch control indicators.

Flight dynamics FIG. 1 shows the flight angles of an aircraft and FIG. 2 the forces and moments acting on an aircraft. In developing the force equations the wind axis reference system is used. In this system, the reference axis is always aligned with the velocity vector of the aircraft, as shown in FIG. 1, where 0, the pitch angle, is defined as the angle between th horizontal and the Wing chord. As shown,

' the angle is the flight path angle measured from the horizon to the wind axis; and the angle of attack is the angle between the wind axis and the wing chord.

If all forces acting on the aircraft are assumed to act through the aircraft center of gravity, their force vectors will be as shown in FIG. 2. The velocity vector V, shown as a reference, is tangent to the flight path and coincident with the wind axis, and is in the direction of flight of the aircraft; drag D is in the opposite direction. The lift L is perpendicular to the wind axis and the weight W is acting along the true vertical. In this particular diagram, the thrust vector T is assumed to act along the wing chord of the aircraft. The moment acts about the center of gravity.

By summing the forces with reference to the wind axis system and summing the moments about the center of gravity, the following equations are derived:

where M is a complex function primarily of V, a and 6 (elevator deflection angle).

From FIG. 2, it can be seen that:

The moment Equation 3 can be neglected when only the maximum aircraft response is considered, because the inertia term only tends to delay any rotational response. In this preliminary analysis, rotational response time is not a factor. Evaluationis based only on relative response magnitudes and, therefore, the momentequation is neglected. With the'remaining equations, it is then possible to represent an aircrafts maximum response characteristics. Under flight conditions where the drag forces (includ ing W components) are less than the thrust forces, the aircraft will have excess thrust. From Equations 1 and 2, it can be shown that this thrust canbe used to produce acceleration either entirely along the flight path, entirely perpendicular to the flight path, or in various combinations between these two extremes. FIG. 3(a) shows the excess thrust available at various airspeeds for a typical cargo aircraft. This excess thrust can then be used to generate the acceleration of (V) values, as shown in FIG. 3(b), or to generate the rate of change of flight path (7) values shown in FIG. 3(a). fore, would be between these maximum values. Since utilization of these two parameters is of prime importance during the initial climb phase, further discussion of these parameters will be continued later.

TAKE-OFF ANALYSIS Any compromise, thereangle or is increased. Since the aircraft is still on the runway, the fiightpath angle is zero and 0t is equal to 0. As at and airspeed increase, the lift'and drag also increase. The increase of the drag force, due to an increase of a and airspeed, only tends to reduce the excess thrust which reduces V. As soon as the lift forces become greater than the gravitational forces, the aircraft will leave the runway and a'y will result. At this time, the transition phase ends and the initial climb phase begins.

Initial climb phase In this phase, the utilization of the excessthrust is of prime importance. As mentioned, this thrust could be used to obtain all 7, all V, or a compromise between the two. Neither extreme is desirable because an increase a y and increase v, but no increase'of V is possible;

Since an increase of V is desired after lift-off, all excess thrust cannot be used to obtain 7. It is also noted that a as 7 increases, the weight component along the flight path increases and reduces the amount of excess thrust A complete take-off can be divided into three distinct phases:

(1) Ground-roll (2) Transition (3) Initial-climb The ground-roll phase begins when the aircraft starts the take-off roll and ends'when rotation speed is obtained. The transition phase. begins when the aircraft has sufficient rotation speed and ends When the aircraft leaves the ground (lift-off). Initial-climb begins after lift-off and continues until flaps are up.

By rotation it is meant that the aircraft physically rotates about its pitch axis, that is, the nose raises and, as shown in FIG. 1, the angles 0 and a are generated. At this time, the aircraft leaves its three-point attitude and assumes an attitude necessary to break ground at the proper lift-off speed. Normally, the lift-off speed (V is 1.2 times the stalling speed of the aircraft (V Although take-oif is possible at speeds nearer to V restrictions such as safety of flight prohibits the use of these speeds. Disturbances, such as gusts or excessive use of controls by the pilot, may cause the airspeed to fall below the stalling speed and level flight will not be maintained Ground-roll phase The purpose of this phase is to accelerate the aircraft to the lift-off velocity as soon as possible, thus reducing the ground-roll distance.

During this phase, only lateral control is necessary and since only longitudinal effects during take-01f are analyzed, the ground-roll phase will not be considered. a

' Transition phase As the airspeed approaches 'V the aircraft is; rotated to the desired lift-off attitude. Thisattitude depends upon the aircraft and the take-off conditions, but normally an attitude is established which would result in a lift-off velocity of approximately 1.2 V As rotation begins, the

available (Equation 1).

Normal takewfi 7 On a typical take-off, the aircraft is accelerated on the runway to the normalrotation speed. As the speed of the aircraft approaches V during the ground roll, the

attitude. As the angle of attack increases, the lift of the aircraft also increasesyuntil finally, as the break-ground speed is attained and the lift-off attitude is established, the lift component of force becomes greater than the gravitational forces and the aircraft leaves the runway. At lift-off, the angle of attack and the angle 0 are equal and 'y is zero. The excess thrust is now used to obtain acceleration of both V and Since .both V and 'y are increasing while the pilot maintains a constant 0, the angle a'decreases. The angle 0 is maintained constant until V +20 knots 'isobtained. At this time, the excess thrust is no longer needed to'accelerate along the flight path, and V is made zero. All the excess thrust is then usedto obtain acceleration of 'y.

The typical initial climb phase, as just explained, appears to be a combination of constant 0 and constant V. This, in effect, is true. However, the use of this type climb is notbased on obtaining the maximum performance for which the aircraft is capable, but rather the maximum performance obtainable with present instru mentation. As will be explained later, take-off performance can be improved with different instrumentation. Since the pilot has only the attitude gyro and, in some cases, an I angle-of-attack indicator, the take-off characteristics obtained by using each of these indicators independently are ofinterest and will be analyzednext.

Present pitch control indicators OL o=12f=6 0 (3) nd= a w=297,000 lbs.

i r ssnoo lbs.

(6) Flaps set. at 30 Gear down Likewise, ac-

Parameter time plots and aircraft altitude-versus-distance plots were recorded. The time plots show the complete parameter reactions for each indicator. The altitude-versus-distance plots show the distance needed to gain 500 feet of altitude. The distance plots also show the flight path obtained with the assumed loss of one engine at various times in the flight.

Constant take-ofi The attitude gyro, which is installed in most aircraft, is a gyroscopic instrument which should give sensitive, reliable information. However, the instrument has several disadvantages, one being that it is sensitive to acceleration forces. Because of the acceleration present during the ground-roll phase, the attitude gyro can precess as much as 7. Even the improved attitude gyros precess as much as 2, which is still too great an error if maximum performance is to be obtained. Besides these objections, the instrument is difficult to read accurately, as small incremental changes are not discernible, and the actual magnitude of 0 can only be approximated. However, neglecting these faults, an analog computer analysis and discussion of a constant 6 take-01f follow. The conditions and techniques of analysis are as stated earlier.

, In this type of take-off, the aircraft rotates to some selected pitch angle at V and maintains this angle constant from lift-off until completion of the initial climb. Just after rotation, the aircraft will have an angle 41 equal to 0 and the flight path angle will be Zero. At this time,

the excess thrust produces a positive V and V increases. This increase in velocity produces additional lift. This excess lift will generate some flight path acceleration and, therefore, some 7. Since 0 is held constant and 'y is increasing, the angle a must decrease. Although a does decrease, the resultant lift continues to increase because V has increased. This trade-off of V' and or continues until the excess thrust is balanced by the drag and weight components, and until 'y and V are zero.

The effects of the contants 9 initial climb are clearly shown on the time plots of FIG. 4. It can be seen that, at lift-off, 'y is zero; a is 12; V is 276 f.p.s.; and V is 2 f.p.s. The flight path angle increases immediately after lift-off, as shown by an increasing 7. Although V increases, the value of V is diminishing. As equilibrium is reached, V goes to zero; 'y remains constant at 4; cc remains constant at 8; and V remains constant at 325 fps. The altitude vs. distance plots of this phase are shown in FIG. 5 for normal and reduced thrust. FIG. 6 shows the effect of various climb angles, and FIG. 7 shows the elfect of rotating the aircraft at various lift-off airspeeds.

Constant cc take-0 Although not in widespread use as an attitude control indicator, the angle-of-attack indicator is a means of controlling the pitch of an aircraft. As an instrument, an angle-of-attack indicator has several advantages over the attitude gyro. The instrument is not acceleration sensitive; therefore, no errors are incurred because-of groundroll acceleration. In addition, the indicator can read directly the magnitude of a and the instrument has a satisfactory accuracy of 0.1". However, one problem does exist: Because the sensor only measures local angle of attack, a position must be found where the relation between local and remote angle of attack is constant, or, in

' other words, the sensor must be mounted on the aircraft at a location where the wind direction at the sensor with respect to the chord of the aircraft, which direction is influenced by the air flow over the aircraft surfaces, has a constant relation to the true wind direction with respect to the chord of the aircraft over the usable range of the angle of attack. However, this is possible within the limits of instrument accuracy. Therefore, under the assumption that the use of an or indicator is entirely feasible,

the explanation of the constant or initial climb phase follows.

In this take-elf, the aircraft rotates to a selected angle of attack at V and maintains this a throughout the initial climb. As in the constant 0 take-off, the excess thrust is producing a positive V at lift-ofl. Since at is held constant, and at V the lift is equal to weight, any increase in V will cause the lift to become greater than the Weight,

resulting in a positive The increase in 'y further reduces the excess thrust available which, in turn, reduces V. Eventually, due to the increasing 7, the excess thrust producing V is exhausted. However, a positive is still generated. This is seen as point 1 in FIG. 8 on the computer time plots. The increase in 7 after V has gone to zero results in an increase in drag components, which further decreases velocity. This decrease in V reduces the lift which, in turn, decreases At point 2 on FIG. 8, the V and, consequently, the lift have been reduced to such an extent as to cause to become zero. Since is still at its peak, the velocity continues to decrease and 7 becomes negative and 'y decreases. V, although negative, is building up until at point 3 of FIG. 8 it becomes positive. As V starts to increase, the lift increases which results in 7 increasing until at point 4, 7 equals zero, V is maximum, and the cycle repeats, thus generating the phugoid path. It can be seen also that the condition which generates this phugoid is the phase relation between 7 and V. It is noted in FIG. 9 that the phugoid is steeper when a is increased, and that it is further aggravated when the velocity is increased as shown in FIG. 10. Certainly, any take-off under these conditions is completely unsatisfactory. However, by comparing the initial climb plot with the constant 0 plot, it was seen that the initial performance of the constant a climb is better. Because of this, the angle-of-attack indicator as a pitch control device during the initial climb phase has an advantage.

INDICATOR DESIGN AND PERFORMANCE In the previous section on flight mechanics, it was shown that numerous flight parameters were available to indicate the take-off performance of an aircraft. In this section, the feasibility of combining these parameters as inputs to an indicator, which can be used by the pilot to guide the aircraft during the take-off phase, is explored.

To assist in the design and evaluation of the various indicators, each indicator was evaluated on the analog computer. From the computer, altitude-versus-distance and parameter-versus-time plots were recorded under conditions of normal and reduced thrust for each indicator. The combination safely producing the maximum altitude in the shortest distance under all thrust conditions was selected for further analysis.

Preliminary considerations Prior to the development of the indicator, several conditions and limitations of the analysis were determined. The ground-roll phase of take-off was not included, because in this phase only lateral control by the pilot is necessary. However, to minimize the ground roll and initiate lift-oil as soon as possible, the aircraft is rotated to the maximum allowable angle of attack just as the lift-off velocity is attained. For the KC- aircraft, a =12 and V =276 f.p.s. This airspeed and angle of attack constitute the initial condition for all indicator evaluations. Since the critical period of take-off was established to be between lift-off and 500 feet, the indicator evaluation was not considered beyond this altitude (initial climb phase). During this period, the aircraft was considered to have had gear down and 30 flaps. In order to simulate the loss of one engine, thrust was reduced 25% at various times during take-off. It was reduced at lift-off, lift-off plus 5 seconds, and lift-off plus 20 seconds. As stated earlier, asymmetric forces were neglected for these power-loss simulations. The results of all runs were compared for each indicator combination.

Parameter selection From theaircraft equations of motion, it was seen that or, 'y, and/ or V could be used to control the aircraft. However, in the indicator design, only cc and V were used because of their sensor availability, faster response, and direct relationship to present control systems. Therefore, in the design of the instrument, the aircrafts attitude was determined on the analog computer by controlling c and/ or V in the equations of motion.

Indicator selection The approaches leading to the indicator development were varied. A complete analytical approach was limited because of the many parameters and their non-linear nature. Besides the analytical approach, three other approaches were used. These were:

. (1) An acceleration-modified approach (2) A velocity-modified approach 7 (3) A pilot technique approach In each of these approaches, a controlling function determined one of the variables in the aircrafts equations of motion (Equations 1 and 2). These controlling functions Were:

1 :12? (2) V=Constant 3 0:12

Each of these controlling functions was incorporated in an indicator which was then analyzed on the analog computer. The performance of each indicator was then compared against the design standards previously mentioned. The results are shown in FIGS. 11a and 11b. It was decided that no single controlling function furnished satisfactory results throughout the initial climb. How

ever, by combining the constant or and the constant velocity controlling functions into one indicator, a maximum takeoff performance could be obtained. The following relates to this selected indicator.

Constant angle of attack By referring to the altitude-versus-distance plot in FIG. 11b and the time plots in FIG. 8, it can be seen that a constant or climb produces maximum performance until V goes to zero. After this, remains positive only at the expense of V. A continuation of constant. results in the phugoid, as explained in the previous section. However, if a constant or take-off is maintained until V goes tozero, then this portion of the climb phase willbe maximized.

Constant velocity 7 'From Equationsl and 2, it can be seen that a maximum climb angle is obtained if all excess thrust is used to produce This means that, with at zero, any excess thrust must necessarily be used to obtain a positive y. Since the constant or portion of the take-offends with V Consequently, any instrument using these and in opposition to the Even neglecting the possibility of the aircraft dragging its. tail, as would happenwith a KC-135, thissituation would also lead to a diflicult control problem for the pilot, since VL is much too slow for the initial climb. An-

other disadvantage of holding V constant isthat the airspeed indicator is unreliable close to the ground. The actual airspeed may be quite different from'an indicated airspeed because of erratic static pressure due to airflow and ground effects. These disadvantages eliminate a constant velocity path without atransition phase; However, if these faults are neglected, the results of using a constant V are shown in FIGS. 12 and 13. j

Therefore, by using constant a to transition from V to the climb velocity and to gain anrinitial altitude, a safe, controllable climb speedcan be established. The results of a constant tat-constant V climb are shown in FIGS. 14 and 15 on the parameter time plots and altitude-versusdistance plots. A comparison withthe other climbs clearly shows the advantages of using the selected indicator.

7 A take-off indicator to direct the take-oft of an aircraft in accordance with the above constant a-constant V program is shown in logical form in FIG. 16. A practical embodiment is shown in FIG. 17. The take-off is accomplished in two phases. The first phase begins with the ground roll, includes lift-off and ends when the aircraft acceleration has fallen to zero. The second phase begins when the first phase ends and extends to the conclusion of the take-off, usually considered to be when the aircraft has attained an altitude of 500 feet.

' Referring to FIG. 16, there are four inputs to the take-off indicator, namely, the acceleration (V) input obtained from acceleration sensor 1t ,the,rate-of-change of pitch (b) input obtained from pitch angle sensor 11,

the angle of attack (a) input'obtained from' angle-oi attack sensor 12 and. the velocity (V) input obtained from air-speed sensor 13. All of these sensors are standard items 'presentlyavailable.

The phase in which the indicator is operating andtheoutput from theV sensor 10 causes the switch actuator' M to operate the switch K to its phase 1 position; During this period there is no change from the horizontal attitude of the aircraft and, consequently, a and' fi are both zero. In phase 1, the output of the 0 sensor is applied through" contact K and level adjusting device. 15 to summing network 16 along with the outputs from the or sensor 12 and the rotation programmer 17. The device 15 is a means'for either decreasing or increasing the magnitude of thesen'sor output as required by the'cha'racteristics of the particular aircraft, The i, and outputsare applied to summing device. 16 in aiding relationship rotation programmer output as indicated by the signs. i m

The programmer 17 has the proper lift-off attitude of the particular aircraft set into it in advance; Its operation is initiated when the aircraft on the runway has reached the proper rotation velocity V This is accomplished by comparing'in circuit 9 the aircraft velocity V from sensor 13 with the velocity V previously set into 

1. APPARATUS FOR DIRECTING THE TAKE-OFF OF AN AIRCRAFT IN TWO SUCCESSIVE PHASESD, SAID APPARATUS COMPRISING: MEANS OPERATIVE DURING THE FIRST OF SAID PHASES FOR COM-/ PARING THE INSTANEOUS ANGLE OF ATTACK OF SAID AIRCRAFT WITH A PREDETERMINED LIFT-OFF ANGLE OF ATTACK AND FOR INDI CATING THE MAGNITUDE AND DIRECTION OF ANY DIFFERENCE, MEANS OPERATIVE DURING THE SECOND OF SAID PHASES FOR COMPARING THE INSTANTANEOUS AIR VELOCITY OF SAID AIRCRAFT WITH A CAPTIVE VELOCITY AND FOR INDICATING THE MAGNITUDE AND DIRECTION OF ANY DIFFERENCE, AND MEANS RESPONSIVE TO THE ACCELERATION OF SAID AIRCRAFT AND OPERATIVE WHEN SAID ACCELERATION EQUALS ZERO TO EFFECT A TRANSITION FROM THE FIRST PHASE TO THE SECOND PHASE AND TO ESTABLISH THE AIR VELOCITY AT THE INSTANT OF TRANSITION AS SAID CAPTIVE VELOCITY. 